Matt Cap Shading texture
Go to Render Settings and switch the render engine to Workbench. This is the render engine the viewport uses and is responsible for matcap lighting.

Then select the Matcap you want to use just like you would do from the viewport by using the Lighting dropdown below the Sampling menu. Once you press render, each frame will be created using the lighting type that you have specified. It also renders lighting fast because Workbench is designed to provide instantaneous shading for the viewport.

No fancy node editor work required, just switch the render engine, choose a matcap, and that's about it.